Saul Kripke, in full Saul Aaron Kripke (born Nov. 13, 1940, Bay Shore, Long Island, N.Y., U.S.), American logician and philosopher who from the 1960s was one of the most powerful thinkers in Anglo-American philosophy (seeanalytic philosophy).

Kripke began his important work on the semantics of modal logic (the logic of modal notions such as necessity and possibility) while he was still a high-school student in Omaha, Neb. A groundbreaking paper from this period, “A Completeness Theorem for Modal Logic,” was published in the Journal of Symbolic Logic in 1959, during Kripke’s freshman year at Harvard University. In 1962 he graduated from Harvard with the only nonhonorary degree he ever received, a B.S. in mathematics. He remained at Harvard until 1968, first as a member of the Harvard Society of Fellows and then as a lecturer. During these years he continued a series of publications extending his original results in modal logic; he also published important papers in intuitionistic logic (the logic underlying the mathematical intuitionism of L.E.J. Brouwer), set theory, and the theory of transfinite recursion (seerecursive function). Kripke taught logic and philosophy at Rockefeller University from 1968 to 1976 and at Princeton University, as McCosh Professor of Philosophy, from 1976 until his retirement in 1998. He delivered the prestigious John Locke Lectures at the University of Oxford in 1973 and received the Rolf Schock Prize in logic and philosophy, awarded by the Royal Swedish Academy of Sciences, in 2001. In 2003 he was appointed distinguished professor at the City University of New York (CUNY).

Naming and Necessity

Kripke’s most important philosophical publication, Naming and Necessity (1980), based on transcripts of three lectures he delivered at Princeton in 1970, changed the course of analytic philosophy. It provided the first cogent account of necessity and possibility as metaphysical concepts, and it distinguished both concepts from the epistemological notions of a posteriori knowledge and a priori knowledge (knowledge acquired through experience and knowledge independent of experience, respectively) and from the linguistic notions of analytictruth and synthetic truth, or truth by virtue of meaning and truth by virtue of fact (seeanalytic proposition). In the course of making these distinctions, Kripke revived the ancient doctrine of essentialism, according to which objects possess certain properties necessarily—without them the objects would not exist at all. On the basis of this doctrine and revolutionary new ideas about the meaning and reference of proper names and of common nouns denoting “natural kinds” (such as heat, water, and tiger), he argued forcefully that some propositions are necessarily true but knowable only a posteriori—e.g., “Water is H2O” and “Heat is mean molecular kinetic energy”—and that some propositions are contingently true (true in some circumstances but not others) but knowable a priori. These arguments overturned the conventional view, inherited from Immanuel Kant (1720–1804), that identified all a priori propositions as necessary and all a posteriori propositions as contingent. Naming and Necessity also had far-reaching implications regarding the question of whether linguistic meaning and the contents of beliefs and other mental states are partly constituted by social and environmental facts external to the individual. According to Kripke’s causal theory of reference, for example, the referent of a given use of a proper name, such as Aristotle, is transmitted through an indefinitely long series of earlier uses; this series constitutes a causal-historical chain that is traceable, in principle, to an original, or “baptismal,” application. Kripke’s view posed a serious challenge to the prevailing “description” theory, which held that the referent of a name is the individual who is picked out by an associated definite description, such as (in the case of Aristotle) the teacher of Alexander the Great. Finally, Kripke’s work contributed greatly to the decline of ordinary language philosophy and related schools, which held that philosophy is nothing more than the logical analysis of language.

In 1975–76 Kripke published important work on the notion of truth and the liar paradox (which involves sentences that say of themselves that they are not true). According to the then-dominant approach, developed by the Polish logician Alfred Tarski, the liar paradox requires giving up the view that a natural language such as English contains a single truth predicate. Instead, there is a hierarchy of predicatestruen for each integer n. The range of each predicate is restricted to that subpart of the language whose sentences contain either no truth predicate at all or truth predicates of a level less than n. Since it follows from this that sentences assessing their own truth or untruth cannot be formulated, inconsistency is avoided, though at the cost of a certain loss of expressive power. Kripke developed a nonhierarchical framework that retained much of this expressive power without surrendering too many of the advantages of Tarski’s theory. Kripke’s approach relied on certain previously known conditions under which languages can contain their own truth predicates and on his own intuitive conception of true as a predicate that is only partially defined—i.e., defined by rules that determine a class of positive cases to which the predicate applies, a class of negative cases to which it does not apply, and a class of cases for which no result can be reached. Although certain problems arising from the liar paradox remained recalcitrant, Kripke’s framework succeeded in inspiring and guiding much subsequent work.

Meaning and skepticism

In later years Kripke wrote several influential papers on linguistic meaning and language use. “Speaker’s Reference and Semantic Reference” (1977), for example, explained discrepancies between what the rules of a language determine the referent of a term to be and what speakers use the term to refer to in particular cases. “A Puzzle About Belief” (1979) generated surprising and paradoxical conclusions from seemingly innocent applications of the principles employed in reporting the beliefs of others, and it derived cautionary lessons about attempts to infer facts about linguistic meaning from analyses of belief-reporting sentences. In Wittgenstein: On Rules and Private Language (1982), Kripke used considerations originating in the Philosophical Investigations (1953) of Ludwig Wittgenstein to raise skeptical questions about whether knowledge of linguistic meaning can be reduced to rule following, or indeed to any objective facts about speakers. Although Kripke himself drew no conclusion on this point, his discussion was widely interpreted as a serious challenge to attempts to explain meaning in purely naturalistic terms.

Although a prolific thinker and problem solver, Kripke chose to publish relatively few of his works. Nevertheless, some of his unpublished papers—on recursion theory, truth, the nature of logic, personal identity, the ontological nature of numbers, colour and colour terms, presupposition, and various paradoxes—have been influential through lectures, seminars, and informal circulation among colleagues and students.